https://ghoshaakash.pages.dev/tags/number-theory/Recent content in Number-Theory on Aakash GhoshHugoen-usSun, 12 Apr 2026 00:00:00 +0000https://ghoshaakash.pages.dev/posts/project-euler-003/Sun, 12 Apr 2026 00:00:00 +0000https://ghoshaakash.pages.dev/posts/project-euler-003/<h2 id="problem">Problem</h2> <p>What is the largest prime factor of the number $n = 600851475143$?</p> <h2 id="key-observation">Key Observation</h2> <p>If $p$ is the smallest prime factor of $n$, then $p \leq \sqrt{n}$. So we only need to trial-divide up to $\sqrt{n}$. After removing all such small factors, whatever remains is the largest prime factor.</p> <p>For $n = 600851475143$, we have $\lfloor \sqrt{n} \rfloor = 775146$, so we need to check at most ~387,000 odd numbers — trivial for a computer.</p>